A NATION CHALLENGED: THE VIDEO; BIN LADEN, ON TAPE, BOASTS OF TRADE CENTER ATTACKS; U.S. SAYS IT PROVES HIS GUILT

The United States released a videotape today showing Osama bin Laden laughing and boasting about the Sept. 11 attacks that killed more than 3,000 people.

On the videotape, Mr. bin Laden describes how the planes that were flown in suicide missions into the World Trade Center towers did far more damage than he ever imagined they would. ''We calculated in advance the number of casualties from the enemy, who would be killed based on the position of the tower,'' he said, speaking in Arabic. English subtitles were provided by the United States government. ''We calculated that the floors that would be hit would be three or four floors. I was the most optimistic of them all.'' [Excerpts, Page B4.]

Bush administration officials said that the amateur videotape, which they believe was filmed on Nov. 9 at a guest house in Kandahar, Afghanistan, was proof that Mr. bin Laden was guilty in the Sept. 11 attacks.

Officials said the tape was found in late November in a house in Jalalabad, Afghanistan, and was turned over to the Central Intelligence Agency. Officials would not say if the United States paid for the tape.

On the tape, Mr. bin Laden, 44, indicated that the men who carried out the plot knew they were on what he called a ''martyrdom operation,'' but did not have details of the mission until the last minute. ''We asked each of them to go to America, but they didn't know anything about the operation, not even one letter,'' Mr. bin Laden said. ''But they were trained, and we did not reveal the operation to them until they are there and just before they boarded the planes.''

Here the tape differed from what administration officials said it would show -- that some of the men thought they were engaged only in a hijacking and did not know they would die.

''There is information that is on those tapes that, again, shows the world just how evil Osama bin Laden is, and how he claims piety, while leading people to deaths that they very well were not aware of,'' Ari Fleischer, the White House spokesman, said on Monday.

Mr. bin Laden also said that Mohamed Atta was the leader of the attacks. ''Mohamed from the Egyptian family was in charge of the group,'' he said, meaning the Al Qaeda Egyptian group.

The New York Times verified the translation with two independent interpreters, who found no significant errors but said that an authoritative translation would require an Arabic transcript. It was impossible to tell from the tape, which jumps among several scenes, if anything was edited.

The hourlong tape shows a smiling and relaxed Mr. bin Laden paying a call on a man referred to in the videotape only as ''sheik,'' who frequently flatters Mr. bin Laden about the success of the attacks, while they eat and converse. The man, identified as a Sheik al-Ghamdi from a tribe in Assir Province, appears paralyzed from the waist down, and offers Mr. bin Laden news and praise from religious figures in Saudi Arabia, which in the videotape emerges as a crucial link to the Al Qaeda terror network.

A senior Saudi official tonight identified Sheik al-Ghamdi and described him as a militant cleric. The official said several of the suicide hijackers were members of the sheik's tribe.

The Saudi government moved quickly to condemn Mr. bin Laden and others referred to on the tape.

''The tape displays the cruel and inhumane face of a murderous criminal who has no respect for the sanctity of human life or the principles of his faith,'' said a statement by Prince Bandar bin Sultan, the Saudi ambassador to the United States. ''Bin Laden and those he mentions in his tape are deviants and renegades who do not represent the Islamic faith or the Saudi people.''

The White House made the tape public after nearly a week of discussion about its contents and in the end gave the task of its formal release to the Department of Defense. The tape was available at 11 a.m., an hour after President Bush renounced the 1972 Anti-Ballistic Missile Treaty.

The groundswell for the release began when The Washington Post first disclosed the existence of the tape on Dec. 9, the same day that Vice President Dick Cheney confirmed some of the tape's contents on NBC's ''Meet the Press.''

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The tension built as the United States indicted Zacarias Moussaoui, the first person to be charged as a conspirator in the Sept. 11 plot, and relentlessly bombed the Tora Bora caves of eastern Afghanistan, where Mr. bin Laden is thought to be hiding.

Administration officials said that the timing of the tape's release was designed neither to draw attention from the ABM Treaty withdrawal, nor to intensify public opinion against Mr. bin Laden as the United States attempts to close in on him.

Mr. Fleischer indicated today that the tape was found by people other than Americans. The Taliban abandoned the city in mid-November. ''The manner in which the tape was acquired would suggest that people were leaving the house in a real big hurry and left it behind,'' he said.

The tape was turned over to the C.I.A., which translated it. The president was informed of its existence on Nov. 29, and saw excerpts at the White House during an intelligence briefing on Nov. 30.

Administration officials said that the president wanted to release the tape as soon as he saw it, but with the caveat that it not compromise intelligence gathering and with the requirement that the C.I.A. double-check its authenticity. By Dec. 7, officials said, the C.I.A. had determined that the tape had not been altered and it was of Mr. bin Laden.

At that point, officials said, the government asked at least two independent interpreters to collaborate on another translation of the videotape and compare it with the one done by the United States government. Pentagon officials said those interpreters were George Michael of the Diplomatic Language Service and Kassem M. Wahba, the Arabic language program coordinator of the School of Advanced International Studies at Johns Hopkins University. Pentagon officials said the two versions were virtually identical.

The C.I.A. ran tests to determine whether the tape had been altered and to determine whether the voice matched Mr. bin Laden's on previous videotapes that he himself had released. In every case, officials said, the matches were identical.

Mr. bin Laden appears in the tape with Ayman al-Zawahiri, his top deputy and the former leader of a faction of the Egyptian Islamic Jihad, and Slaiman abou-Ghaithc, a spokesman for Mr. bin Laden.

At one point Mr. bin Laden recites poetry and the men discuss their dreams and those of their friends. Mr. bin Laden recounts, for example, the dream of a year ago from a friend who told him, '' 'We were playing a soccer game against the Americans. When our team showed up in the field, they were all pilots!' He said: 'So I wondered if that was a soccer game or a pilot game?' ''

He also recounts the moments when he first heard of the Sept. 11 attacks and apparently mentions where he was. But government officials said that that portion of the tape is inaudible. In the tape, Mr. bin Laden gives a full description of listening to the radio as he and others heard the news that a plane had hit the World Trade Center.

''They were overjoyed when the first plane hit the building, so I said to them: be patient,'' Mr. bin Laden recounted. Then, he told of hearing that the second tower had been hit, as well as the the Pentagon. He made no mention of the fourth plane, which crashed in a field in Pennsylvania.

Intelligence officials said that they were struck by the unprofessional, home-movie quality of the tape and said its purpose was unclear. One said it did not appear the tape was designed for propaganda purposes or that Mr. bin Laden intended it for viewing outside his inner circle.